Some subjects I try to avoid in this blog. But this one seems to become increasingly difficult to escape. Since my interview at Philosophy-To-Go, I regularly get questions about the physics of free will. These questions range from

"Does free will exist given that the laws of physics are deterministic?"

to the more suggestive

"Is our free will based on quantum indeterminism?"

and the more confrontational

"Should physicists not worry given that their theories are incapable of accommodating free will?"

These are all valid questions, but also tricky questions. Simple reason is that topics like 'consciousness' and 'free will' can send us down a muddy track that leads straight into meta-physical quicksands. 

Simply put, there is no physics theory of free will. Physics has a lot to say about the world around us, but contributes little to poorly-defined subjects such as free will. As I stated in the interview at Philosophy-To-Go:

"When it comes to issues like free will and consciousness, physics simply has no answers."

Modern physics has delivered consistent and well-tested theories for many complex phenomena. Not so for free will. Lacking even a generally accepted definition for the very concept of 'free will', physics can not contribute much. However, that does not mean physics is necessarily at odds with free will.  So let me give you here my personal perspective on the question: "Are the laws of physics compatible with the concept of free will?" I do not claim to be an authority on 'the physics of free will', but having read (and tossed away) a few papers on the subject, I really wonder who is.

A lot of confused reasoning has been penned down. No doubt many will judge my present contribution to contribute to the overall confusion. That is fine. You can all comment to this more speculative blogpost, and all constructive criticism is welcome.

So here goes.

Quantum Hopes

Newton's laws of physics are perfectly deterministic. Cause and effect work out such that Newtonian dynamics always leads from a given initial state to a unique final state. Multiple possibilities for a final state never emerge, let alone a choice between multiple final states.

One state at a given time yields one state at a later time. Add Einstein's relativity to the mix, and nothing changes: 'now' and 'then' remain in a one-to-one mapping. All of classical physics (covering Newton's laws and their relativistic extensions) is ruled by determinism. And in a fully deterministic world, free will can not exist. Or at least that is how the standard argument goes.

Those who accept this reasoning tend to turn their hopes to quantum physics. Funnily enough, the dynamic laws of quantum physics are unitary. This means that quantum dynamics - just like classical dynamics - realizes a one-to-one mapping between initial and final states. Quantum dynamics is fully deterministic.

Wait a second, what about the Heisenberg uncertainty principle? Doesn't this principle clearly state that quantum physics is indeterministic? Sure, the uncertainty principle specifies an indeterminism present in quantum physics, but this indeterminism has nothing to do with the dynamics of quantum systems. This is an important observation relevant to the present discussion. There is no indeterminism in the evolution of quantum systems. Indeterminism enters the description only when the quantum system is assumed to interact with a classical system.

This is what presumably happens in a measurement device, and what leads to the infamous measurement problem in quantum physics. Many people seeking a safe place for the concept of free will in 'the house of physics' seem to be content with this place in the cellar where the measurement problem is hiding. As long as quantum physics contains an element of indeterminism, there is supposedly enough room for free will to emerge.

There are a number of problems associated with this approach. Most important issue is that the indeterminism associated with the measurement problem in quantum physics takes the shape of random indeterminism. And adding randomness into the picture only brings us further from free will. A random selection between multiple choices can hardly qualify as free will. 

One might object that some (as of yet undiscovered) dynamics can be hidden in the randomness associated with the measurement problem. A bit like the digits of pi which, although following from a deterministic computational process, appear random in any test. This measurement dynamics could in some way be coupled to consciousness or to anything that conceivably is related to free will. All of this is very vague and hand-waving and goes against current theories. But more importantly: assuming such a speculative free-will dynamics to hide behind measurement indeterminacy does not bring us closer to marrying physics with free will.

As John Conway and Simon Kochen have shown, if there is such a thing as a freedom of choice that results from measurement indeterminacy, then this freedom is a feature that not only humans but also electrons and other elementary particles get their share of.  This result makes it pretty difficult to accept a freedom of choice that could be associated with measurement indeterminacy as explanation for free will. This brings us back to square one.

Gravity to the rescue

If the indeterminism in quantum physics is not going to help us, we are forced to focus once more on the incompatibility between determinism and free will. Are these two concepts really incompatible? 

The relevant question to start from is: given the deterministic laws, can we predict the behavior of arbitrary complex systems? You might answer: "if the system under study is really complex, it would require a computer considerably larger than any existing computer. But yes, when given the means to build a large enough computer, we could - at least in principle - predict the behavior of any system no matter how complex."

But the truth is we can not. Not even in principle. There are systems that are too complex for their behavior to be predicted. And this limitation does not constitute a practical limitation, but a very fundamental one. This was discussed in my previous blogpost God, Godel, Gravity. The point is: predicting the system's behavior requires us to compute the future state more quickly than nature does. For that, we need to build a computer that outpaces nature. If we would attempt building a computer capable of doing so, we would soon discover that this computer collapses and forms a black hole long before it reaches the required size. And this constitutes not just a practical problem, but is the inevitable fate of any attempt to outpace nature. No matter from which components we would built the ultimate computer, and no matter whether this computer uses electrons or photon for processing, we will always run into the same problems.

The thing is: given the fundamental laws of physics, for a system of sufficient complexity you can not predict its future. For that to happen you need a shortcut to describe the deterministic evolution of our universe. However, such a shortcut does not exist. It takes the computing power of the whole universe to 'play out' the universe. Outperforming this computation would require an amount of computing power that simply can not fit into our universe.

Key factor in the above argument is that the system needs to be 'sufficiently complex'. In practice this means that he system needs to have a strong tendency of amplifying tiny causes into large effects. A human brain - with eyes and ears connected to it - certainly has that tendency. As a result, the brain in a living human being can not be assumed to be isolated from the rest of the universe. To predict its behavior, you need to predict the future of the universe in all its details. This, as we have seen, is a fundamental impossibility.

Faking free will

Now you might interject: "Right, complex systems like human brains might be too complex to predict, but that leads us at best to a fake free will. There is still these underlying deterministic laws of physics that determine what the future states of the brain will be."  This remark represents a misconception and a gross underestimation of the fundamental nature of unpredictability. There is absolutely no way one could ever distinguish between 'fake' and 'real' unpredictability. And if it is fundamentally impossible to distinguish between the two, the two are operationally the same. Unpredictability is unpredictability, no matter if there is an underlying deterministic dynamics or not. And unpredictability is free will. What else could you want to have as basis for free will?

You might try another route to escape the above logic: "Even if we can't outpace the universe and therefore can not predict the behavior of a complex system, surely we can postdict it. Such a prediction-after-the-fact would still reveal the underlying determinism and allow us to distinguish 'true free will' from 'fake free will'. Again, this represents a misconception. If prediction of the universe is not possible, neither is postdiction.

The point is that in your simulation you can not start from an arbitrary state. Obtaining such a state for the universe in all its details would again involve colossal energies and lead to to a gravitational collapse. Also here, nature shows us the most efficient way to obtain a certain state: start from the very beginning - the big bang configuration - and 'play it out'.  But if you have to start from the big bang, you will never reach 'now' the moment you want to predict after the fact. To reach this point in the simulation would require a simulation at least as big as the universe. A fundamental impossibility.

The conclusion is inevitable: there is no basis for the postulate that free will is at odds with determinism. Free will and determinism are fully compatible. This is akin to the description of an object as a particle and a wave: since the advent of quantum mechanics we know these are two compatible sides of the same coin.

These were today's thoughts from the armchair. Now, if you don't mind I get back into my hammock to think about real physics.

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The Hammock Physicist on: What's Wrong With E=m.c²?, What's Wrong With 'Relativity'? Entropic Gravity, Entropic Force, Shut Down LHC?, Game Theory, Metric Vs Imperial, Big Bang, Dark Energy, Chaos And Time's Arrow, The Grand Arena, Square Root Of The Universe, Physics In A Nutshell, The Longest Path, Hotel Boltzmann, Quantum Telepathy, Quantum Viruses, QHD, Fibonacci Chaos, Counting A Black Hole, Entropic Everything, God, Godel, Gravity, Holographic Automata, Who Is Today's Einstein?